The game of Set is a simple but addictive card game played with a special 81-card deck. A standard "folklore question" among players of this game is: what is the largest number of cards that can be on the table which do not allow a legal play? I'll explain how this question, which seems to be about cards, is actually a very deep one about geometry over a finite field, and what it has to do with many other popular questions in number theory, and some less popular ones I’m trying to popularize. I will also try to give a sense of why this problem was so hard (until it wasn’t) and how mathematicians approach hard problems.